Generalized local and nonlocal master equations for some stochastic processes

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• 作者：Yanxiang Zhao^a ; ^{yxzhao@email.gwu.edu" class="auth_mail" title="E-mail the corresponding author} ; Jiakou Wang^b ; ^{jiakou.wang@uwalumni.com" class="auth_mail" title="E-mail the corresponding author} ; Yanping Ma^c ; ^{yma@lmu.edu" class="auth_mail" title="E-mail the corresponding author} ; Qiang Du^d ; ^{qd2125@columbia.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlocal flux ; Stochastic coagulation ; Smoluchowski equation ; Conservation law ; Nonlocal diffusion ; Fractional diffusion
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：71
• 期：11
• 页码：2497-2512
• 全文大小：437 K

文摘

In this paper, we present a study on generalized local and nonlocal equations for some stochastic processes. By considering the net flux change in a region determined by the transition probability, we derive the master equation to describe the evolution of the probability density function. Some examples, such as classical Fokker–Planck equations, models for Lévy process, and stochastic coagulation equations, are provided as illustrations. A particular application is a consistent derivation of coupled dynamical systems for spatially inhomogeneous stochastic coagulation processes.